Question

question 3 of 10
the circle below is centered at the point (8, 4) and has a radius of length 4.
what is its equation?
a. $(x - 4)^2+(y + 8)^2 = 4$
b. $(x + 8)^2+(y - 4)^2 = 16$
c. $(x - 4)^2+(y - 8)^2 = 4^2$
d. $(x - 8)^2+(y - 4)^2 = 16$

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given the center \((8,4)\), so \(h = 8\), \(k = 4\). The radius \(r = 4\), then \(r^2=16\).

Step3: Substitute the values into the standard form

Substitute \(h = 8\), \(k = 4\), and \(r^2 = 16\) into \((x - h)^2+(y - k)^2=r^2\), we get \((x - 8)^2+(y - 4)^2=16\).

Answer:

D. \((x - 8)^2+(y - 4)^2=16\)